# Spherical Bessel Function yn (G Dataflow)

Version:
Last Modified: January 9, 2017

Calculates the spherical Bessel function of the second kind.  ## x

The input argument.

Default: 0 ## n

Order of the spherical Bessel function. ## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error ## yn(x)

Value of the spherical Bessel function of the second kind. ## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Calculating the Spherical Bessel Function of the Second Kind

For the spherical Bessel function of the second kind of order n, yn(x) is a solution to the following differential equation.

${x}^{2}\frac{{d}^{2}w}{d{x}^{2}}+2x\frac{dw}{dx}+\left({x}^{2}-n\left(n+1\right)\right)w=0$

The following equation shows the relationship of the spherical Bessel function of the second kind to the Bessel function of the second kind.

${y}_{n}\left(x\right)=\sqrt{\frac{\pi }{2x}}{Y}_{v}\left(x\right),v=n+\frac{1}{2}$

The function is defined according to the following intervals for the input values.

$n\in \Im ,x\in \left[0,\infty \right)$

This node supports the entire domain of this function that produces real-valued results. For any integer value of order n, the function is defined for nonnegative real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported